Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 34

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Figure 2.5 General scheme for stationary data reconciliation and fault detection and isolation (FDI)

not be anything between minus and plus infinity, because of physical inequality
constraints. Without pretending that this is a statistically correct statement, it is in
practice observed that this criterion is sufficiently powerful for improving data at
industrial or even lab scales. Alternative techniques such as LMI [21], robust esti-
mators [60], and artificial neural networks have also been proposed [17-20],[61].
In parallel with the reconciliation procedure, Figure 2.5 also shows optional FDI
procedures. Redundancy equations R are obtained by elimination of X between the
measurement equations and state constraints. Because of the conflict generated by
the uncertainties e and ε, these equations generate residual values that are not zero
but functions of e and ε. These residuals can be used to detect measurement biases
or abnormal deviations to mass and energy conservation laws. These concepts will
be discussed later on in Section 2.12. In Figure 2.5, the term V X is the variance

matrix of the reconciled values that will be discussed in Section 2.9.
The stationary optimization problem defined by Equation 2.30 degenerates into
two limit reconciliation problems when e or ε are assumed to have null values: the
steady-state case and the node imbalance case.
Steady-state data reconciliation. The SSR case is obtained by setting V ε to zero,
thus removing the second term of the criterion. As already said the steady-state case
is an ideal situation. There is a continuum between the stationary and the steady-
sate case, and one can superficially say that SSR is legitimate when V ε is small in
comparison with V .
Node imbalance data reconciliation. At the other end of the relative values of
V and V ε spectra, one may consider the case where the measurement values are
much more accurate than the conservation constraints. In other words V is small
in comparison with V ε .Thefirst term of the reconciliation criterion disappears and
only the residuals ε are estimated. These estimates are called the reconciled node
imbalances.
The feasibility of reconciliation procedures is governed by process observability
[62, 63] and, its corollary, information redundancy. These two concepts are now
discussed briefly.